The Tombuntu blog points out a few settings in Compiz's advanced settings manager, one that doesn't come pre-installed in Ubuntu, but can be easily plugged into the Preferences menu. Once you've got access to Compiz's finer tunings, you'll want to look up what the optimum vertical refresh rate of your monitor is. If you find that, set Compiz to use that refresh rate, and enable the "Sync to Vblank" option. In simple terms, that sets Compiz to draw on the screen only when the monitor is refreshing, give you less skipping when moving windows and reducing jagged cutting in videos.

As noted at the link, this tip won't help systems with lower-end graphics cards that can barely handle desktop effects. Those with serious graphics cards, however, can up the refresh rate higher than their monitor's default if they want an even smoother go of it.